Optimized aerodynamic profile for a turbine vane, in particular for a nozzle of a turbine

ABSTRACT

When cold and in the non-coated state, the aerodynamic profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y, Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point under consideration from a first reference plane P0 situated at the base of the nominal profile, and H is the height of said profile measured from the first reference plane to a second reference plane P1. The measurements D and H are taken radially relative to the axis of the turbine, while the X coordinate is measured in the axial direction of the turbine.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims the benefit of priority to U.S. Patent Application No. 62/504,553, filed on May 11, 2017, the entirety of which is incorporated by reference herein.

INTRODUCTION

The present disclosure relates to an aerodynamic profile for a turbine vane.

In particular, the disclosure relates to the aerodynamic profile of a nozzle vane forming a portion of the stator of a gas turbine, and more particularly of a low pressure turbine of the type used in a turbojet of an aircraft.

The disclosure relates in particular to a nozzle vane of a turbine having a plurality of stages, preferably five stages.

Such a profile should enable the turbine to provide the desired efficiency, and in order to do that it must be such that the flow of air around the profile is sound over the working spectrum of the turbine, i.e. substantially such that it does not give rise to turbulence, which is harmful for overall efficiency.

It must be capable of being installed properly in the environment of the engine, and in particular, for a nozzle vane forming a portion of the stator of the turbine, it must be capable of being fastened easily to the sectors of the foot platform (the zone of the vane that is furthest from the axis of rotation of the turbine) and of the head platform (the zone that is closest to said axis). Furthermore, this part must present a profile enabling it to be manufactured in a reliable and cost-effective manner by available manufacturing methods, such as casting, forging, machining, additive fabrication, or else weaving, without this list being limitative.

Furthermore, the profile of the vane must enable it to withstand the mechanical stresses, to which the vane is subjected, by enabling those stresses to be spread over the entire vane in such a manner as to avoid premature wear thereof. This spreading must apply both in static mode and in dynamic mode.

An object of the disclosure is to propose an aerodynamic profile for a turbine vane that is optimized, and capable of satisfying those objectives.

This object is achieved by the fact that when cold and in a non-coated state, said profile is substantially identical to a nominal profile determined by the Cartesian coordinates X,Y,Zadim given in Table 1, in which the coordinate Zadim is the quotient D/H where D is the distance of the point P under consideration from a reference X,Y plane situated at the base of the nominal profile, and H is the height of said profile measured from said reference plane that is the intersection of the stacking axis of the vane and the axisymmetric surface of the hub, out to a second reference plane that is the intersection of said stacking axis with the axisymmetric surface of the casing, the measurements D and H being taken radially relative to the axis of the turbine, while the coordinate X is measured in the axial direction of the turbine.

This profile has been determined as a result of numerous tests and simulations. It is defined cold, i.e. at an ambient temperature of 20° C. That is a reference temperature at which the profile is geometrically determined. The above-mentioned objectives of aerodynamics and mechanical optimization are naturally valid for the conditions of use of this aerodynamic profile, i.e. when hot, at a temperature that is stabilized when the engine of which the turbine forms a part is being used under cruising conditions.

Furthermore, the aerodynamic profile of the disclosure is defined in the non-coated state. Since turbine vanes are subjected to high temperature gradients, it is common practice for them to be provided with a coating having thermal properties enabling them more easily to withstand such temperature variations. The profile is determined prior to installing such a coating.

It is stated above that the profile of the disclosure is “substantially identical” to the nominal profile. This means that the profile may depart very slightly from said nominal profile.

The aerodynamic profile is thus preferably defined within an envelope of ±1 millimeter (mm) in a direction normal to the surface of the nominal profile.

It is also preferable for the X,Y coordinates of the aerodynamic profile to lie within a range of ±5% relative to the X,Y coordinates of the nominal profile.

In addition, the aerodynamic profile may be positioned rotated within ±10°, particularly within ±5°, more particularly within ±3°, with respect to the radial axis of the vane, along which the coordinate Zadim is measured.

These variations take account in particular to at least one of manufacturing tolerances of the profile, the setting of the profile to adapt to the environment when in operation, and possible deformation occurring when mounting the vane and integrating the same in the nozzle.

With a nozzle vane, i.e. a portion of the stator of a turbine, the profile serves to orient the fluid correctly for the turbine blades that are situated downstream, and that belong in particular to the rotary wheel of the same stage of the turbine.

BRIEF DESCRIPTION OF THE DRAWINGS

The disclosure can be better understood and its advantages appear better on reading the following detailed description of an embodiment given by way of non-limiting example. The description refers to the accompanying drawings, in which:

FIG. 1 is a fragmentary axial diagrammatic section view of a turbine including a vane of profile that corresponds to that of the present disclosure;

FIG. 2 shows a vane of the turbine.

DETAILED DESCRIPTION

The turbine shown in axial section in FIG. 1 comprises five stages referenced respectively S1 to S5. In the direction DF going from upstream to downstream, each stage comprises a nozzle that forms a portion of the stator of the turbine and that has a plurality of radially-oriented vanes, and a rotary wheel that forms a portion of the rotor of the turbine and that likewise includes a plurality of radially-oriented blades.

In FIG. 1, the vanes of the nozzles of stages S1 to S5 are given references N1 to N5 (these vanes are shown in dashed lines, for ease of representation), whereas the blades of rotary wheels of stages S1 to S5 are given respective references W1 to W5.

In known manner, the vanes of the nozzles are fastened at both ends to stationary structure portions, while the blades of the rotary wheels are fastened to a rotary disk via their roots that are formed at their radially-inner ends closer to the axis of the rotation A of the turbine. The disks forming parts of the wheels W1 to W5 are constrained to rotate together.

The disclosure relates a vane of one of the nozzles of the turbine that, as mentioned above, preferably comprises five stages as shown, without this number being limiting.

As best seen in FIG. 2, via its foot 10, which is its end remote from the axis of rotation A, the vane is fastened to the outer ring of the turbine, which ring is stationary in rotation. Via its head 14, formed by its end closer to the axis of rotation A, the vane is fastened to an inner shroud of the turbine. By convention, the aerodynamic profile 18 of the vane is the entire portion of said vane that extends radially outwards from its head 14 to its foot 10 without incorporating the fastenings respectively to the outer ring and to the inner shroud.

In FIG. 2, there can be seen a frame of reference comprising Cartesian coordinates X,Y,Z. The radial direction Z is the height direction of the vane, which extends radially from its head to its foot. This direction Z is perpendicular to the axial direction X which is the direction of the axis of rotation A of the turbine. The direction Y is perpendicular to the X,Z plane and is therefore tangential to the direction of rotation of the turbine.

The nominal profile from which the aerodynamic profile of the disclosure is determined is defined in following Table 1 of coordinates, in which the coordinate Zadim, measured along the axis Z is non-dimensional, whereas the dimensions X and Y, respectively measured along the axes X and Y, are expressed in millimeters.

TABLE 1 X Y Zadim −14.6484 −1.71963 −0.15 −14.6626 −1.77394 −0.15 −14.6656 −1.85547 −0.15 −14.636 −1.97786 −0.15 −14.5541 −2.133 −0.15 −14.4094 −2.31067 −0.15 −14.2004 −2.50601 −0.15 −13.9278 −2.71782 −0.15 −13.5906 −2.9438 −0.15 −13.1878 −3.18055 −0.15 −12.7186 −3.42377 −0.15 −12.1824 −3.66687 −0.15 −11.5792 −3.90258 −0.15 −10.9103 −4.12313 −0.15 −10.1779 −4.31952 −0.15 −9.38528 −4.48207 −0.15 −8.53734 −4.60072 −0.15 −7.64047 −4.66468 −0.15 −6.70287 −4.66166 −0.15 −5.73537 −4.57697 −0.15 −4.75223 −4.39588 −0.15 −3.77154 −4.10549 −0.15 −2.81304 −3.70102 −0.15 −1.89404 −3.18861 −0.15 −1.027 −2.58182 −0.15 −0.2181 −1.8991 −0.15 0.529406 −1.15759 −0.15 1.217763 −0.37598 −0.15 1.850831 0.429447 −0.15 2.433004 1.244755 −0.15 2.968475 2.0582 −0.15 3.461236 2.85963 −0.15 3.915193 3.640115 −0.15 4.333458 4.392168 −0.15 4.718367 5.109506 −0.15 5.071657 5.786847 −0.15 5.394442 6.419947 −0.15 5.687356 7.005428 −0.15 5.951249 7.540502 −0.15 6.187314 8.02296 −0.15 6.39619 8.451604 −0.15 6.577689 8.826427 −0.15 6.73326 9.14756 −0.15 6.863492 9.416348 −0.15 6.969494 9.634942 −0.15 7.051999 9.806612 −0.15 7.06293 9.948483 −0.15 7.024698 10.04015 −0.15 6.98329 10.08718 −0.15 6.943994 10.11497 −0.15 6.904683 10.13268 −0.15 6.849803 10.14445 −0.15 6.761304 10.13531 −0.15 6.653494 10.06726 −0.15 6.570201 9.918344 −0.15 6.470881 9.724702 −0.15 6.347821 9.487124 −0.15 6.199466 9.203988 −0.15 6.023198 8.875196 −0.15 5.81767 8.500751 −0.15 5.58037 8.082191 −0.15 5.309203 7.621646 −0.15 5.002591 7.12173 −0.15 4.658932 6.58587 −0.15 4.276787 6.018169 −0.15 3.854941 5.423305 −0.15 3.392504 4.80654 −0.15 2.888747 4.173744 −0.15 2.343178 3.531389 −0.15 1.755408 2.886718 −0.15 1.12572 2.247274 −0.15 0.455093 1.62083 −0.15 −0.25491 1.015535 −0.15 −1.00181 0.439558 −0.15 −1.78217 −0.09908 −0.15 −2.59208 −0.59179 −0.15 −3.42635 −1.03045 −0.15 −4.27815 −1.40857 −0.15 −5.13944 −1.72101 −0.15 −6.00116 −1.96473 −0.15 −6.85337 −2.13979 −0.15 −7.68617 −2.24882 −0.15 −8.49019 −2.29688 −0.15 −9.25716 −2.29109 −0.15 −9.98019 −2.24045 −0.15 −10.6542 −2.15569 −0.15 −11.2758 −2.04795 −0.15 −11.8437 −1.92923 −0.15 −12.3574 −1.80979 −0.15 −12.8175 −1.69846 −0.15 −13.225 −1.6028 −0.15 −13.5811 −1.52929 −0.15 −13.8871 −1.48452 −0.15 −14.143 −1.4714 −0.15 −14.3471 −1.49317 −0.15 −14.495 −1.5464 −0.15 −14.5849 −1.61459 −0.15 −14.7017 −0.84489 −0.075 −14.723 −0.89803 −0.075 −14.737 −0.98006 −0.075 −14.7241 −1.10786 −0.075 −14.6617 −1.27558 −0.075 −14.5383 −1.47407 −0.075 −14.3518 −1.6984 −0.075 −14.1018 −1.94647 −0.075 −13.7872 −2.21559 −0.075 −13.4066 −2.50247 −0.075 −12.9583 −2.80177 −0.075 −12.4415 −3.1076 −0.075 −11.8553 −3.41211 −0.075 −11.1996 −3.70569 −0.075 −10.4754 −3.97749 −0.075 −9.68502 −4.21498 −0.075 −8.83237 −4.40395 −0.075 −7.92384 −4.52943 −0.075 −6.96863 −4.57633 −0.075 −5.97908 −4.52989 −0.075 −4.97109 −4.37586 −0.075 −3.9638 −4.10428 −0.075 −2.97816 −3.71106 −0.075 −2.03258 −3.20336 −0.075 −1.13913 −2.59758 −0.075 −0.30401 −1.91324 −0.075 0.47122 −1.16998 −0.075 1.188922 −0.3867 −0.075 1.853736 0.419495 −0.075 2.470274 1.234432 −0.075 3.042372 2.046512 −0.075 3.573684 2.845639 −0.075 4.067491 3.623044 −0.075 4.526324 4.371336 −0.075 4.95199 5.084317 −0.075 5.345247 5.757032 −0.075 5.70615 6.385662 −0.075 6.034593 6.967076 −0.075 6.331651 7.498203 −0.075 6.597742 7.977108 −0.075 6.833354 8.402604 −0.075 7.038439 8.774607 −0.075 7.2142 9.093329 −0.075 7.361359 9.360088 −0.075 7.481139 9.577023 −0.075 7.574638 9.747324 −0.075 7.596812 9.890755 −0.075 7.563349 9.986375 −0.075 7.523631 10.03644 −0.075 7.484895 10.06661 −0.075 7.446503 10.08598 −0.075 7.392329 10.10005 −0.075 7.303751 10.09485 −0.075 7.19349 10.03149 −0.075 7.102156 9.88791 −0.075 6.992024 9.700885 −0.075 6.855959 9.471354 −0.075 6.692436 9.1977 −0.075 6.49909 8.879828 −0.075 6.273338 8.518577 −0.075 6.012805 8.115613 −0.075 5.715305 7.673364 −0.075 5.379285 7.194656 −0.075 5.003542 6.682914 −0.075 4.586787 6.142447 −0.075 4.128022 5.578102 −0.075 3.626856 4.995114 −0.075 3.082885 4.399497 −0.075 2.496249 3.797587 −0.075 1.86768 3.196031 −0.075 1.19813 2.602102 −0.075 0.489379 2.023049 −0.075 −0.25586 1.465913 −0.075 −1.03386 0.937204 −0.075 −1.8401 0.443005 −0.075 −2.66989 −0.01011 −0.075 −3.51776 −0.41601 −0.075 −4.37741 −0.76932 −0.075 −5.24164 −1.06602 −0.075 −6.10243 −1.30408 −0.075 −6.95134 −1.48347 −0.075 −7.78007 −1.60525 −0.075 −8.58068 −1.67081 −0.075 −9.34549 −1.6831 −0.075 −10.0674 −1.64668 −0.075 −10.7404 −1.5689 −0.075 −11.3599 −1.45871 −0.075 −11.9233 −1.32687 −0.075 −12.4296 −1.18449 −0.075 −12.8799 −1.04258 −0.075 −13.2762 −0.91175 −0.075 −13.6218 −0.80179 −0.075 −13.919 −0.71923 −0.075 −14.1698 −0.67033 −0.075 −14.3743 −0.66094 −0.075 −14.5278 −0.69262 −0.075 −14.6248 −0.74956 −0.075 −14.6056 −1.70814 0 −14.6279 −1.76221 0 −14.6434 −1.84574 0 −14.6335 −1.97651 0 −14.5717 −2.14845 0 −14.4477 −2.35232 0 −14.2587 −2.58261 0 −14.0038 −2.83629 0 −13.6818 −3.11015 0 −13.2911 −3.40033 0 −12.8307 −3.70176 0 −12.2993 −4.00782 0 −11.6964 −4.31013 0 −11.0217 −4.59781 0 −10.276 −4.85822 0 −9.46213 −5.07647 0 −8.58465 −5.2351 0 −7.65171 −5.31604 0 −6.67531 −5.30242 0 −5.67132 −5.17953 0 −4.6591 −4.93585 0 −3.66024 −4.56578 0 −2.69672 −4.0702 0 −1.7877 −3.45818 0 −0.94285 −2.75037 0 −0.16592 −1.96827 0 0.545588 −1.13386 0 1.19696 −0.26649 0 1.794912 0.617137 0 2.346488 1.5028 0 2.857049 2.379191 0 3.330222 3.237189 0 3.769482 4.068644 0 4.177988 4.866363 0 4.557227 5.624668 0 4.908169 6.338711 0 5.231344 7.004538 0 5.527299 7.618775 0 5.793511 8.180217 0 6.031933 8.686258 0 6.242999 9.135777 0 6.426846 9.528613 0 6.584395 9.865195 0 6.716331 10.14689 0 6.823744 10.37598 0 6.9077 10.55571 0 6.92424 10.70296 0 6.884398 10.79842 0 6.840508 10.84671 0 6.798819 10.87455 0 6.759101 10.89094 0 6.704044 10.90077 0 6.6162 10.88882 0 6.511524 10.81677 0 6.42951 10.66783 0 6.331028 10.47462 0 6.209509 10.23731 0 6.063649 9.954149 0 5.891487 9.624671 0 5.689154 9.250201 0 5.453671 8.832565 0 5.183146 8.373829 0 4.875565 7.876941 0 4.529446 7.345341 0 4.143089 6.783425 0 3.715369 6.195951 0 3.24571 5.588098 0 2.733766 4.9656 0 2.179217 4.334932 0 1.582517 3.702741 0 0.944752 3.07586 0 0.267537 2.461354 0 −0.44637 1.865794 0 −1.19244 1.294199 0 −1.96616 0.75185 0 −2.76257 0.243799 0 −3.57635 −0.22518 0 −4.40149 −0.65125 0 −5.23142 −1.03173 0 −6.0591 −1.36526 0 −6.87758 −1.65105 0 −7.68037 −1.88769 0 −8.46186 −2.07065 0 −9.21596 −2.19494 0 −9.93546 −2.25791 0 −10.6124 −2.262 0 −11.2394 −2.21613 0 −11.8113 −2.13212 0 −12.3255 −2.02348 0 −12.7817 −1.90357 0 −13.1816 −1.785 0 −13.5281 −1.679 0 −13.8243 −1.59387 0 −14.074 −1.54033 0 −14.2779 −1.52507 0 −14.4313 −1.55655 0 −14.5284 −1.61327 0 −14.6052 −1.45341 0.100003 −14.6333 −1.50645 0.100003 −14.6579 −1.59018 0.100003 −14.6616 −1.72485 0.100003 −14.6166 −1.90706 0.100003 −14.5093 −2.12747 0.100003 −14.3365 −2.38 0.100003 −14.0963 −2.66056 0.100003 −13.787 −2.96539 0.100003 −13.4071 −3.29025 0.100003 −12.9551 −3.62969 0.100003 −12.4294 −3.97658 0.100003 −11.8287 −4.32184 0.100003 −11.1521 −4.65322 0.100003 −10.3993 −4.95557 0.100003 −9.57209 −5.21043 0.100003 −8.67513 −5.39595 0.100003 −7.71774 −5.48886 0.100003 −6.71493 −5.46778 0.100003 −5.68689 −5.31754 0.100003 −4.657 −5.02941 0.100003 −3.64942 −4.60284 0.100003 −2.68703 −4.04388 0.100003 −1.78594 −3.36929 0.100003 −0.95438 −2.60106 0.100003 −0.19225 −1.76355 0.100003 0.505324 −0.87919 0.100003 1.144853 0.033186 0.100003 1.733581 0.957556 0.100003 2.279367 1.879901 0.100003 2.787003 2.789685 0.100003 3.259269 3.678449 0.100003 3.699824 4.538035 0.100003 4.111037 5.361675 0.100003 4.494194 6.143749 0.100003 4.849973 6.879486 0.100003 5.178525 7.565047 0.100003 5.478249 8.198018 0.100003 5.749443 8.775778 0.100003 5.992591 9.296389 0.100003 6.207888 9.758828 0.100003 6.395719 10.16281 0.100003 6.556631 10.50897 0.100003 6.691381 10.79868 0.100003 6.801075 11.03429 0.100003 6.886961 11.21906 0.100003 6.908985 11.36966 0.100003 6.869469 11.46829 0.100003 6.824259 11.51778 0.100003 6.781056 11.54579 0.100003 6.740324 11.56163 0.100003 6.684074 11.57015 0.100003 6.59517 11.55506 0.100003 6.492193 11.47693 0.100003 6.409474 11.32504 0.100003 6.308611 11.12885 0.100003 6.184406 10.88775 0.100003 6.035623 10.59992 0.100003 5.860599 10.26471 0.100003 5.65602 9.883119 0.100003 5.419206 9.456754 0.100003 5.148566 8.987466 0.100003 4.842237 8.478014 0.100003 4.4989 7.93166 0.100003 4.116854 7.352669 0.100003 3.694968 6.745673 0.100003 3.232494 6.115839 0.100003 2.728723 5.469008 0.100003 2.183083 4.811697 0.100003 1.596087 4.150318 0.100003 0.968215 3.492063 0.100003 0.300892 2.843992 0.100003 −0.40341 2.212835 0.100003 −1.14082 1.604325 0.100003 −1.90695 1.023938 0.100003 −2.69712 0.477104 0.100003 −3.50601 −0.03139 0.100003 −4.3281 −0.49672 0.100003 −5.15661 −0.91636 0.100003 −5.98412 −1.28948 0.100003 −6.80423 −1.61371 0.100003 −7.61196 −1.88277 0.100003 −8.40175 −2.08969 0.100003 −9.16698 −2.22697 0.100003 −9.8989 −2.29076 0.100003 −10.5875 −2.28536 0.100003 −11.2237 −2.22074 0.100003 −11.8015 −2.11142 0.100003 −12.3182 −1.97395 0.100003 −12.7741 −1.82433 0.100003 −13.171 −1.67455 0.100003 −13.5131 −1.53737 0.100003 −13.805 −1.42287 0.100003 −14.0515 −1.3413 0.100003 −14.2557 −1.30158 0.100003 −14.4144 −1.31625 0.100003 −14.5181 −1.36447 0.100003 −14.6608 −0.22344 0.199999 −14.6953 −0.27453 0.199999 −14.7298 −0.3572 0.199999 −14.7505 −0.49391 0.199999 −14.7268 −0.68508 0.199999 −14.644 −0.92261 0.199999 −14.4959 −1.19958 0.199999 −14.2806 −1.51157 0.199999 −13.9958 −1.85442 0.199999 −13.6396 −2.22357 0.199999 −13.2097 −2.61318 0.199999 −12.7039 −3.01584 0.199999 −12.1195 −3.4208 0.199999 −11.4539 −3.81456 0.199999 −10.7055 −4.17943 0.199999 −9.87428 −4.49286 0.199999 −8.96395 −4.72743 0.199999 −7.98466 −4.85239 0.199999 −6.95529 −4.83916 0.199999 −5.9024 −4.67035 0.199999 −4.85489 −4.34254 0.199999 −3.83785 −3.86638 0.199999 −2.86884 −3.26159 0.199999 −1.95805 −2.55087 0.199999 −1.10834 −1.75835 0.199999 −0.31769 −0.90654 0.199999 0.417744 −0.01459 0.199999 1.102295 0.901428 0.199999 1.73971 1.828182 0.199999 2.335195 2.753018 0.199999 2.892273 3.665709 0.199999 3.412759 4.557955 0.199999 3.899059 5.42184 0.199999 4.35328 6.250334 0.199999 4.775558 7.038126 0.199999 5.166799 7.780066 0.199999 5.527567 8.471904 0.199999 5.857487 9.110509 0.199999 6.156746 9.693211 0.199999 6.424931 10.21843 0.199999 6.662704 10.68487 0.199999 6.870933 11.09195 0.199999 7.049212 11.44083 0.199999 7.19847 11.73283 0.199999 7.319941 11.9703 0.199999 7.415141 12.1565 0.199999 7.450256 12.30869 0.199999 7.41701 12.41255 0.199999 7.37276 12.46523 0.199999 7.328995 12.49485 0.199999 7.285402 12.51175 0.199999 7.225035 12.51949 0.199999 7.130933 12.4982 0.199999 7.026696 12.40748 0.199999 6.93372 12.24752 0.199999 6.817358 12.04223 0.199999 6.674223 11.78988 0.199999 6.502982 11.48853 0.199999 6.302609 11.13712 0.199999 6.072564 10.73513 0.199999 5.811374 10.2835 0.199999 5.519031 9.783124 0.199999 5.194932 9.236012 0.199999 4.838949 8.644617 0.199999 4.450364 8.012452 0.199999 4.02933 7.343111 0.199999 3.575522 6.641151 0.199999 3.087788 5.912253 0.199999 2.564041 5.163395 0.199999 2.00151 4.402871 0.199999 1.398056 3.63946 0.199999 0.753284 2.881531 0.199999 0.068042 2.137274 0.199999 −0.65597 1.414937 0.199999 −1.41614 0.722641 0.199999 −2.21049 0.07021 0.199999 −3.03736 −0.5305 0.199999 −3.89382 −1.06686 0.199999 −4.77456 −1.52647 0.199999 −5.67211 −1.89699 0.199999 −6.57631 −2.16599 0.199999 −7.47309 −2.32475 0.199999 −8.34505 −2.37456 0.199999 −9.17519 −2.32419 0.199999 −9.94947 −2.18938 0.199999 −10.6588 −1.99097 0.199999 −11.2994 −1.7507 0.199999 −11.8713 −1.48885 0.199999 −12.3772 −1.22214 0.199999 −12.8203 −0.96299 0.199999 −13.2046 −0.72163 0.199999 −13.5348 −0.5061 0.199999 −13.8186 −0.32736 0.199999 −14.0626 −0.19459 0.199999 −14.2705 −0.11532 0.199999 −14.4405 −0.10357 0.199999 −14.5575 −0.13959 0.199999 −14.6291 2.178163 0.300001 −14.6666 2.12828 0.300001 −14.7072 2.047182 0.300001 −14.7386 1.91073 0.300001 −14.7301 1.715859 0.300001 −14.6642 1.469791 0.300001 −14.5306 1.181226 0.300001 −14.3297 0.854131 0.300001 −14.0571 0.494415 0.300001 −13.712 0.106162 0.300001 −13.2915 −0.30405 0.300001 −12.793 −0.72831 0.300001 −12.2132 −1.15517 0.300001 −11.5489 −1.56974 0.300001 −10.7981 −1.95335 0.300001 −9.96058 −2.28155 0.300001 −9.04007 −2.52396 0.300001 −8.04819 −2.64851 0.300001 −7.00606 −2.62497 0.300001 −5.94303 −2.4356 0.300001 −4.89001 −2.08006 0.300001 −3.87128 −1.57486 0.300001 −2.9014 −0.94467 0.300001 −1.98738 −0.21456 0.300001 −1.13049 0.59169 0.300001 −0.32819 1.452641 0.300001 0.423435 2.350054 0.300001 1.12794 3.26902 0.300001 1.787584 4.19751 0.300001 2.406701 5.123396 0.300001 2.988515 6.036519 0.300001 3.534699 6.928553 0.300001 4.046852 7.791906 0.300001 4.52633 8.61982 0.300001 4.973564 9.406684 0.300001 5.388525 10.14775 0.300001 5.77181 10.83862 0.300001 6.123135 11.47606 0.300001 6.442133 12.05762 0.300001 6.728954 12.58138 0.300001 6.983372 13.04647 0.300001 7.205592 13.45266 0.300001 7.396105 13.80064 0.300001 7.555707 14.09183 0.300001 7.685641 14.32862 0.300001 7.787549 14.51425 0.300001 7.829271 14.6668 0.300001 7.798406 14.77282 0.300001 7.755091 14.82738 0.300001 7.711719 14.85873 0.300001 7.667464 14.8775 0.300001 7.605641 14.8872 0.300001 7.508544 14.86682 0.300001 7.402171 14.77264 0.300001 7.301702 14.61111 0.300001 7.17487 14.40426 0.300001 7.019115 14.14986 0.300001 6.833187 13.84582 0.300001 6.616297 13.49092 0.300001 6.368017 13.08454 0.300001 6.088064 12.62695 0.300001 5.776489 12.11905 0.300001 5.43321 11.56257 0.300001 5.058786 10.95963 0.300001 4.652624 10.31375 0.300001 4.215211 9.628388 0.300001 3.746179 8.908201 0.300001 3.244981 8.158554 0.300001 2.711036 7.385395 0.300001 2.143585 6.595443 0.300001 1.540471 5.79709 0.300001 0.901234 4.998211 0.300001 0.224388 4.20834 0.300001 −0.49201 3.438554 0.300001 −1.24905 2.700665 0.300001 −2.04588 2.006284 0.300001 −2.88184 1.36949 0.300001 −3.75449 0.805502 0.300001 −4.65816 0.329248 0.300001 −5.58356 −0.04551 0.300001 −6.51747 −0.30753 0.300001 −7.44292 −0.45041 0.300001 −8.34059 −0.47496 0.300001 −9.19165 −0.39174 0.300001 −9.98069 −0.21731 0.300001 −10.6974 0.027611 0.300001 −11.3367 0.320961 0.300001 −11.8992 0.64016 0.300001 −12.3893 0.965143 0.300001 −12.8146 1.277626 0.300001 −13.1829 1.564242 0.300001 −13.501 1.815579 0.300001 −13.7764 2.022959 0.300001 −14.0162 2.178284 0.300001 −14.2241 2.273749 0.300001 −14.3981 2.293378 0.300001 −14.5196 2.260207 0.300001 −14.8617 2.776317 0.399997 −14.8972 2.72404 0.399997 −14.934 2.639845 0.399997 −14.9585 2.500156 0.399997 −14.9408 2.303361 0.399997 −14.8616 2.057742 0.399997 −14.7147 1.771028 0.399997 −14.4946 1.450512 0.399997 −14.2015 1.099583 0.399997 −13.8328 0.7242 0.399997 −13.3866 0.330381 0.399997 −12.8604 −0.07315 0.399997 −12.2511 −0.47414 0.399997 −11.5564 −0.85705 0.399997 −10.7754 −1.20248 0.399997 −9.9087 −1.48409 0.399997 −8.96264 −1.67072 0.399997 −7.9516 −1.72827 0.399997 −6.90061 −1.62585 0.399997 −5.84266 −1.34805 0.399997 −4.81054 −0.89819 0.399997 −3.82801 −0.2969 0.399997 −2.90713 0.427549 0.399997 −2.05193 1.247904 0.399997 −1.26076 2.13932 0.399997 −0.52836 3.079954 0.399997 0.151808 4.051327 0.399997 0.784364 5.039169 0.399997 1.373817 6.031018 0.399997 1.924157 7.016002 0.399997 2.439365 7.984292 0.399997 2.921901 8.927619 0.399997 3.373455 9.838759 0.399997 3.79581 10.71108 0.399997 4.189757 11.53899 0.399997 4.555234 12.3179 0.399997 4.89287 13.04355 0.399997 5.202554 13.71268 0.399997 5.484005 14.32282 0.399997 5.737224 14.8722 0.399997 5.961962 15.35995 0.399997 6.158263 15.78592 0.399997 6.326626 16.15084 0.399997 6.467711 16.45621 0.399997 6.582604 16.70453 0.399997 6.672753 16.89918 0.399997 6.707088 17.05568 0.399997 6.669344 17.16098 0.399997 6.621893 17.21321 0.399997 6.575845 17.24183 0.399997 6.529783 17.25754 0.399997 6.46663 17.26261 0.399997 6.370307 17.23413 0.399997 6.271476 17.12961 0.399997 6.181016 16.95959 0.399997 6.066355 16.74233 0.399997 5.925721 16.47506 0.399997 5.758101 16.15554 0.399997 5.562888 15.78242 0.399997 5.339747 15.35501 0.399997 5.088605 14.87344 0.399997 4.809468 14.33863 0.399997 4.502511 13.75212 0.399997 4.168293 13.116 0.399997 3.806153 12.43368 0.399997 3.416569 11.70852 0.399997 2.998731 10.94526 0.399997 2.552129 10.14895 0.399997 2.075754 9.32551 0.399997 1.567979 8.481771 0.399997 1.026971 7.625318 0.399997 0.450888 6.764392 0.399997 −0.16228 5.908144 0.399997 −0.81583 5.067679 0.399997 −1.51228 4.25494 0.399997 −2.2519 3.481599 0.399997 −3.03573 2.762142 0.399997 −3.8631 2.112446 0.399997 −4.73031 1.548948 0.399997 −5.62966 1.087447 0.399997 −6.54886 0.741781 0.399997 −7.47084 0.520897 0.399997 −8.37521 0.427379 0.399997 −9.24061 0.452391 0.399997 −10.0488 0.579559 0.399997 −10.7871 0.786596 0.399997 −11.4493 1.04885 0.399997 −12.0348 1.342089 0.399997 −12.5472 1.645261 0.399997 −12.9923 1.940749 0.399997 −13.3777 2.214117 0.399997 −13.7104 2.454439 0.399997 −13.9973 2.653438 0.399997 −14.2456 2.801778 0.399997 −14.4574 2.895576 0.399997 −14.6344 2.905748 0.399997 −14.7552 2.865026 0.399997 −14.5899 4.807465 0.5 −14.6301 4.75812 0.5 −14.6739 4.676639 0.5 −14.7102 4.538542 0.5 −14.7095 4.339595 0.5 −14.6501 4.086642 0.5 −14.526 3.786977 0.5 −14.3331 3.446265 0.5 −14.0689 3.06936 0.5 −13.7307 2.661501 0.5 −13.3157 2.229273 0.5 −12.8206 1.781396 0.5 −12.2416 1.329588 0.5 −11.5751 0.889532 0.5 −10.818 0.481842 0.5 −9.96929 0.133366 0.5 −9.03291 −0.12318 0.5 −8.02148 −0.252 0.5 −6.95875 −0.22052 0.5 −5.87748 −0.01147 0.5 −4.81108 0.373043 0.5 −3.78454 0.912805 0.5 −2.81119 1.579347 0.5 −1.89614 2.345058 0.5 −1.03882 3.184754 0.5 −0.2351 4.076236 0.5 0.520687 5.000517 0.5 1.23186 5.943425 0.5 1.901942 6.892359 0.5 2.534327 7.8361 0.5 3.131404 8.765098 0.5 3.694893 9.670971 0.5 4.225902 10.54636 0.5 4.725121 11.38481 0.5 5.192782 12.18072 0.5 5.628375 12.92951 0.5 6.031832 13.62707 0.5 6.402621 14.2702 0.5 6.740003 14.8566 0.5 7.043757 15.38451 0.5 7.313487 15.85313 0.5 7.549293 16.26228 0.5 7.751553 16.61274 0.5 7.92105 16.90596 0.5 8.059068 17.14437 0.5 8.167399 17.33122 0.5 8.217922 17.48444 0.5 8.189753 17.59348 0.5 8.146974 17.65021 0.5 8.103475 17.68318 0.5 8.058816 17.70327 0.5 7.996037 17.71433 0.5 7.896879 17.6948 0.5 7.789205 17.59808 0.5 7.682704 17.43619 0.5 7.547074 17.22956 0.5 7.380776 16.97523 0.5 7.182638 16.67102 0.5 6.952025 16.31558 0.5 6.688728 15.90812 0.5 6.392702 15.44879 0.5 6.064338 14.93828 0.5 5.703938 14.37816 0.5 5.312374 13.77036 0.5 4.889502 13.11824 0.5 4.436258 12.42501 0.5 3.952304 11.69541 0.5 3.437622 10.93452 0.5 2.892094 10.14802 0.5 2.314511 9.342968 0.5 1.703683 8.527019 0.5 1.058526 7.708426 0.5 0.377755 6.896394 0.5 −0.34124 6.102316 0.5 −1.10004 5.338133 0.5 −1.89847 4.615808 0.5 −2.7366 3.94982 0.5 −3.61282 3.356045 0.5 −4.52248 2.850745 0.5 −5.45697 2.449331 0.5 −6.40318 2.164691 0.5 −7.3436 2.004853 0.5 −8.25774 1.970343 0.5 −9.12494 2.052676 0.5 −9.92777 2.234649 0.5 −10.6547 2.493287 0.5 −11.3009 2.802903 0.5 −11.8672 3.139666 0.5 −12.3586 3.482208 0.5 −12.7824 3.813065 0.5 −13.147 4.118031 0.5 −13.4608 4.386539 0.5 −13.7316 4.610255 0.5 −13.9676 4.780477 0.5 −14.1737 4.889179 0.5 −14.3501 4.915637 0.5 −14.4751 4.886613 0.5 −14.591 4.859979 0.600003 −14.63 4.80937 0.600003 −14.6723 4.726763 0.600003 −14.7068 4.587722 0.600003 −14.7037 4.388136 0.600003 −14.6414 4.134998 0.600003 −14.5141 3.835481 0.600003 −14.3178 3.495197 0.600003 −14.0499 3.11903 0.600003 −13.7075 2.712341 0.600003 −13.2878 2.281932 0.600003 −12.7872 1.836757 0.600003 −12.202 1.389084 0.600003 −11.5283 0.955166 0.600003 −10.7632 0.556441 0.600003 −9.90636 0.219939 0.600003 −8.96261 −0.02147 0.600003 −7.94562 −0.13229 0.600003 −6.88 −0.08326 0.600003 −5.79857 0.14369 0.600003 −4.73391 0.543855 0.600003 −3.70931 1.095509 0.600003 −2.73785 1.771742 0.600003 −1.82298 2.54386 0.600003 −0.96373 3.387314 0.600003 −0.15591 4.2805 0.600003 0.606134 5.204809 0.600003 1.325514 6.146446 0.600003 2.00527 7.093259 0.600003 2.648473 8.034264 0.600003 3.257799 8.959697 0.600003 3.834134 9.861686 0.600003 4.378221 10.73304 0.600003 4.890968 11.56712 0.600003 5.372191 12.35851 0.600003 5.820974 13.10286 0.600003 6.237126 13.79606 0.600003 6.619977 14.43498 0.600003 6.96864 15.01739 0.600003 7.282793 15.54156 0.600003 7.5619 16.00676 0.600003 7.80599 16.41287 0.600003 8.015422 16.76066 0.600003 8.190973 17.05162 0.600003 8.333948 17.28818 0.600003 8.446177 17.47356 0.600003 8.50128 17.62576 0.600003 8.475129 17.73569 0.600003 8.433311 17.79343 0.600003 8.390353 17.82739 0.600003 8.345933 17.84853 0.600003 8.283117 17.861 0.600003 8.183119 17.84353 0.600003 8.073742 17.74771 0.600003 7.96345 17.5873 0.600003 7.822677 17.38275 0.600003 7.65014 17.13091 0.600003 7.444677 16.82958 0.600003 7.205686 16.47736 0.600003 6.933009 16.07342 0.600003 6.626702 15.61785 0.600003 6.287279 15.11126 0.600003 5.915196 14.55513 0.600003 5.511403 13.95139 0.600003 5.075974 13.30327 0.600003 4.610057 12.61389 0.600003 4.113684 11.8878 0.600003 3.586776 11.13017 0.600003 3.029011 10.34689 0.600003 2.439852 9.544603 0.600003 1.81846 8.730762 0.600003 1.163787 7.913602 0.600003 0.474258 7.102587 0.600003 −0.25216 6.308594 0.600003 −1.01684 5.543268 0.600003 −1.82011 4.818902 0.600003 −2.66197 4.149696 0.600003 −3.54061 3.550846 0.600003 −4.45192 3.038671 0.600003 −5.38774 2.628515 0.600003 −6.3355 2.333368 0.600003 −7.27829 2.161584 0.600003 −8.19608 2.114303 0.600003 −9.06842 2.18374 0.600003 −9.87778 2.353498 0.600003 −10.6122 2.601129 0.600003 −11.2664 2.901471 0.600003 −11.8407 3.230594 0.600003 −12.3397 3.566926 0.600003 −12.7691 3.894576 0.600003 −13.1364 4.19976 0.600003 −13.4513 4.469898 0.600003 −13.7224 4.695716 0.600003 −13.9627 4.86237 0.600003 −14.1768 4.957079 0.600003 −14.3548 4.978493 0.600003 −14.4789 4.94399 0.600003 −14.8397 3.100511 0.699999 −14.8736 3.046327 0.699999 −14.9083 2.960096 0.699999 −14.9307 2.818381 0.699999 −14.9125 2.619323 0.699999 −14.8308 2.37134 0.699999 −14.676 2.084529 0.699999 −14.4531 1.760396 0.699999 −14.156 1.405926 0.699999 −13.7822 1.02685 0.699999 −13.329 0.630485 0.699999 −12.7934 0.226581 0.699999 −12.1723 −0.17185 0.699999 −11.4634 −0.54776 0.699999 −10.6653 −0.879 0.699999 −9.78082 −1.1388 0.699999 −8.81788 −1.29501 0.699999 −7.7936 −1.31538 0.699999 −6.73481 −1.1732 0.699999 −5.67381 −0.8589 0.699999 −4.64016 −0.38042 0.699999 −3.65357 0.239802 0.699999 −2.72308 0.974141 0.699999 −1.85089 1.796681 0.699999 −1.03444 2.683991 0.699999 −0.26866 3.615718 0.699999 0.452718 4.574263 0.699999 1.132478 5.546971 0.699999 1.77422 6.521964 0.699999 2.381161 7.488691 0.699999 2.955944 8.437832 0.699999 3.499791 9.361563 0.699999 4.01333 10.25298 0.699999 4.497524 11.10557 0.699999 4.952163 11.91406 0.699999 5.376498 12.67404 0.699999 5.77027 13.38153 0.699999 6.132806 14.03342 0.699999 6.46322 14.62749 0.699999 6.761157 15.16205 0.699999 7.026036 15.6364 0.699999 7.257841 16.05042 0.699999 7.45684 16.40496 0.699999 7.623725 16.70154 0.699999 7.759702 16.94264 0.699999 7.866476 17.13157 0.699999 7.918568 17.28509 0.699999 7.889543 17.39446 0.699999 7.846069 17.45109 0.699999 7.802093 17.48385 0.699999 7.75692 17.50379 0.699999 7.693542 17.51445 0.699999 7.593735 17.49401 0.699999 7.487313 17.39415 0.699999 7.381307 17.23003 0.699999 7.245858 17.02085 0.699999 7.079934 16.76331 0.699999 6.882473 16.45511 0.699999 6.652947 16.09483 0.699999 6.391268 15.6816 0.699999 6.097589 15.21544 0.699999 5.772441 14.69698 0.699999 5.416332 14.12765 0.699999 5.030172 13.50938 0.699999 4.614241 12.84526 0.699999 4.169438 12.13853 0.699999 3.695948 11.39355 0.699999 3.193113 10.61576 0.699999 2.661522 9.810335 0.699999 2.100081 8.984072 0.699999 1.507538 8.144469 0.699999 0.882664 7.299604 0.699999 0.224514 6.45805 0.699999 −0.46962 5.63062 0.699999 −1.2018 4.828859 0.699999 −1.97258 4.064466 0.699999 −2.78238 3.350924 0.699999 −3.63009 2.702698 0.699999 −4.51266 2.135459 0.699999 −5.42339 1.664184 0.699999 −6.35155 1.302268 0.699999 −7.28203 1.058976 0.699999 −8.19631 0.937453 0.699999 −9.07455 0.932697 0.699999 −9.89866 1.031033 0.699999 −10.6552 1.212098 0.699999 −11.3364 1.452598 0.699999 −11.9408 1.728353 0.699999 −12.4705 2.018331 0.699999 −12.9303 2.305463 0.699999 −13.3268 2.574659 0.699999 −13.6683 2.81285 0.699999 −13.9618 3.011078 0.699999 −14.2148 3.159617 0.699999 −14.4357 3.239651 0.699999 −14.6156 3.242723 0.699999 −14.736 3.195574 0.699999 −14.979 0.057595 0.800001 −15.0054 −0.00078 0.800001 −15.0285 −0.091 0.800001 −15.0326 −0.23468 0.800001 −14.9899 −0.43036 0.800001 −14.8791 −0.66733 0.800001 −14.6945 −0.93663 0.800001 −14.4347 −1.23304 0.800001 −14.0987 −1.55211 0.800001 −13.6852 −1.88894 0.800001 −13.1906 −2.23428 0.800001 −12.6127 −2.5775 0.800001 −11.9498 −2.90464 0.800001 −11.2011 −3.19754 0.800001 −10.368 −3.43287 0.800001 −9.45687 −3.5841 0.800001 −8.48022 −3.62178 0.800001 −7.45906 −3.51816 0.800001 −6.42163 −3.25496 0.800001 −5.39793 −2.82934 0.800001 −4.41287 −2.25319 0.800001 −3.4813 −1.5494 0.800001 −2.60888 −0.74365 0.800001 −1.79558 0.140233 0.800001 −1.03766 1.080941 0.800001 −0.3294 2.059907 0.800001 0.335185 3.061375 0.800001 0.960055 4.072848 0.800001 1.547919 5.083781 0.800001 2.102971 6.083662 0.800001 2.62816 7.063487 0.800001 3.124239 8.015996 0.800001 3.592293 8.93428 0.800001 4.033506 9.811953 0.800001 4.447666 10.64386 0.800001 4.834369 11.42549 0.800001 5.193369 12.15294 0.800001 5.524006 12.82314 0.800001 5.825474 13.43383 0.800001 6.097477 13.98333 0.800001 6.339534 14.47086 0.800001 6.551507 14.89638 0.800001 6.733593 15.26075 0.800001 6.886377 15.56555 0.800001 7.010924 15.81333 0.800001 7.10876 16.0075 0.800001 7.155313 16.16309 0.800001 7.122466 16.2716 0.800001 7.076665 16.32654 0.800001 7.0312 16.35739 0.800001 6.984878 16.37523 0.800001 6.920693 16.38268 0.800001 6.821587 16.35682 0.800001 6.719997 16.25096 0.800001 6.621274 16.08114 0.800001 6.495121 15.86468 0.800001 6.34064 15.5982 0.800001 6.156889 15.27937 0.800001 5.943407 14.9067 0.800001 5.700141 14.47934 0.800001 5.42731 13.99727 0.800001 5.125427 13.46114 0.800001 4.794982 12.87239 0.800001 4.436686 12.23308 0.800001 4.050969 11.54612 0.800001 3.638368 10.81495 0.800001 3.199184 10.04378 0.800001 2.732661 9.237926 0.800001 2.238931 8.402712 0.800001 1.717407 7.544394 0.800001 1.165909 6.670732 0.800001 0.583365 5.789358 0.800001 −0.03134 4.908544 0.800001 −0.68095 4.038448 0.800001 −1.3681 3.190244 0.800001 −2.09367 2.37498 0.800001 −2.85829 1.605008 0.800001 −3.6621 0.894385 0.800001 −4.50324 0.257955 0.800001 −5.37676 −0.28962 0.800001 −6.27381 −0.73514 0.800001 −7.18144 −1.06856 0.800001 −8.08311 −1.28498 0.800001 −8.96027 −1.38621 0.800001 −9.79469 −1.38257 0.800001 −10.5714 −1.29124 0.800001 −11.2804 −1.13376 0.800001 −11.9172 −0.9322 0.800001 −12.4815 −0.7081 0.800001 −12.9763 −0.47975 0.800001 −13.4062 −0.26216 0.800001 −13.7769 −0.06762 0.800001 −14.0945 0.093271 0.800001 −14.3661 0.208365 0.800001 −14.5973 0.256995 0.800001 −14.7764 0.231462 0.800001 −14.8892 0.166844 0.800001 −15.0696 0.044819 0.899997 −15.0928 −0.01481 0.899997 −15.1116 −0.10585 0.899997 −15.1101 −0.24935 0.899997 −15.0605 −0.44304 0.899997 −14.9424 −0.67591 0.899997 −14.7501 −0.93913 0.899997 −14.4849 −1.22981 0.899997 −14.1435 −1.54195 0.899997 −13.7231 −1.86871 0.899997 −13.2212 −2.20154 0.899997 −12.6356 −2.52904 0.899997 −11.9646 −2.83629 0.899997 −11.2081 −3.10446 0.899997 −10.3691 −3.31143 0.899997 −9.45479 −3.43111 0.899997 −8.47909 −3.43787 0.899997 −7.4624 −3.31019 0.899997 −6.42999 −3.03486 0.899997 −5.40697 −2.61246 0.899997 −4.41357 −2.05476 0.899997 −3.46231 −1.38123 0.899997 −2.55917 −0.61315 0.899997 −1.70542 0.228834 0.899997 −0.8992 1.125766 0.899997 −0.13682 2.060576 0.899997 0.585682 3.018559 0.899997 1.270365 3.988088 0.899997 1.919552 4.958405 0.899997 2.536393 5.91911 0.899997 3.122602 6.861488 0.899997 3.678295 7.778378 0.899997 4.204432 8.662643 0.899997 4.70147 9.508027 0.899997 5.168664 10.30954 0.899997 5.605536 11.06258 0.899997 6.01145 11.76335 0.899997 6.385502 12.40886 0.899997 6.726715 12.99694 0.899997 7.034656 13.52594 0.899997 7.308706 13.99517 0.899997 7.548698 14.40461 0.899997 7.754878 14.75511 0.899997 7.927886 15.04823 0.899997 8.068928 15.28647 0.899997 8.179713 15.47313 0.899997 8.237914 15.62445 0.899997 8.213647 15.735 0.899997 8.172204 15.79315 0.899997 8.129237 15.82725 0.899997 8.08421 15.84854 0.899997 8.020517 15.86065 0.899997 7.919464 15.84191 0.899997 7.810363 15.74307 0.899997 7.699599 15.58003 0.899997 7.55829 15.37211 0.899997 7.385139 15.1161 0.899997 7.179033 14.80972 0.899997 6.939397 14.45155 0.899997 6.666093 14.04073 0.899997 6.359379 13.57722 0.899997 6.019691 13.0617 0.899997 5.647766 12.49547 0.899997 5.244287 11.88068 0.899997 4.810195 11.22 0.899997 4.345957 10.51705 0.899997 3.852451 9.775817 0.899997 3.329487 9.001562 0.899997 2.777194 8.199836 0.899997 2.195929 7.376602 0.899997 1.584465 6.539442 0.899997 0.941926 5.696268 0.899997 0.268255 4.854991 0.899997 −0.4379 4.025263 0.899997 −1.17808 3.21786 0.899997 −1.95255 2.443623 0.899997 −2.76043 1.71365 0.899997 −3.60068 1.040641 0.899997 −4.47064 0.437855 0.899997 −5.36506 −0.08189 0.899997 −6.27562 −0.50721 0.899997 −7.19076 −0.82951 0.899997 −8.09601 −1.04456 0.899997 −8.97524 −1.15382 0.899997 −9.81242 −1.16565 0.899997 −10.5939 −1.09464 0.899997 −11.3101 −0.95933 0.899997 −11.9559 −0.7806 0.899997 −12.5308 −0.57875 0.899997 −13.0367 −0.3713 0.899997 −13.4777 −0.17316 0.899997 −13.8591 0.002892 0.899997 −14.1868 0.145336 0.899997 −14.4667 0.24155 0.899997 −14.7016 0.272274 0.899997 −14.8791 0.23333 0.899997 −14.987 0.160224 0.899997 −15.1981 −0.64584 1 −15.2129 −0.70795 1 −15.2198 −0.80048 1 −15.2011 −0.94248 1 −15.1293 −1.12867 1 −14.985 −1.34567 1 −14.7667 −1.58694 1 −14.474 −1.84867 1 −14.1036 −2.12429 1 −13.6536 −2.40705 1 −13.1224 −2.68813 1 −12.5082 −2.9549 1 −11.811 −3.19245 1 −11.0326 −3.3817 1 −10.1784 −3.50135 1 −9.25853 −3.52851 1 −8.28851 −3.44257 1 −7.28846 −3.2286 1 −6.28035 −2.88083 1 −5.28429 −2.40325 1 −4.31568 −1.80776 1 −3.38427 −1.11082 1 −2.49575 −0.32936 1 −1.65194 0.519295 1 −0.85177 1.418477 1 −0.09263 2.352895 1 0.62829 3.309141 1 1.311769 4.276688 1 1.960945 5.244274 1 2.577852 6.20229 1 3.163914 7.142207 1 3.719739 8.056576 1 4.2461 8.938375 1 4.743452 9.781357 1 5.210783 10.58069 1 5.64799 11.33157 1 6.054348 12.03026 1 6.428916 12.6738 1 6.770721 13.26 1 7.079333 13.78722 1 7.354137 14.25478 1 7.594885 14.6627 1 7.801822 15.01183 1 7.975538 15.30377 1 8.11721 15.54101 1 8.228512 15.72686 1 8.288226 15.87725 1 8.265674 15.98794 1 8.225055 16.0465 1 8.182597 16.08106 1 8.13763 16.10296 1 8.073795 16.11579 1 7.972156 16.09785 1 7.861914 15.99935 1 7.749798 15.83624 1 7.607102 15.62798 1 7.432211 15.37157 1 7.22395 15.06477 1 6.981716 14.70615 1 6.705304 14.2949 1 6.394983 13.83097 1 6.051074 13.31512 1 5.674377 12.74862 1 5.265359 12.13377 1 4.825293 11.47304 1 4.354224 10.77036 1 3.853392 10.02952 1 3.322746 9.255724 1 2.762288 8.454667 1 2.172117 7.632553 1 1.551959 6.796358 1 0.901272 5.953794 1 0.219594 5.113127 1 −0.49324 4.283057 1 −1.23835 3.473903 1 −2.01607 2.696375 1 −2.82455 1.960224 1 −3.6623 1.276899 1 −4.52655 0.658252 1 −5.4124 0.115613 1 −6.31243 −0.34103 1 −7.2166 −0.70405 1 −8.11251 −0.96939 1 −8.98621 −1.13752 1 −9.82346 −1.21467 1 −10.6115 −1.21273 1 −11.3405 −1.14766 1 −12.0044 −1.03756 1 −12.6008 −0.90116 1 −13.1301 −0.75491 1 −13.5944 −0.61297 1 −13.997 −0.48694 1 −14.342 −0.38855 1 −14.6354 −0.34086 1 −14.873 −0.35331 1 −15.0399 −0.42729 1 −15.1334 −0.51868 1 −15.2374 −1.71686 1.075002 −15.2423 −1.7805 1.075002 −15.2354 −1.873 1.075002 −15.1966 −2.01082 1.075002 −15.0997 −2.18519 1.075002 −14.9284 −2.38138 1.075002 −14.6824 −2.59421 1.075002 −14.3596 −2.81747 1.075002 −13.9584 −3.04572 1.075002 −13.4778 −3.27198 1.075002 −12.9167 −3.48684 1.075002 −12.2753 −3.67838 1.075002 −11.5549 −3.8304 1.075002 −10.7597 −3.9245 1.075002 −9.89763 −3.94106 1.075002 −8.98128 −3.85999 1.075002 −8.02746 −3.66543 1.075002 −7.05581 −3.34764 1.075002 −6.08507 −2.90713 1.075002 −5.13147 −2.35039 1.075002 −4.20667 −1.68964 1.075002 −3.3182 −0.93938 1.075002 −2.47146 −0.11348 1.075002 −1.66836 0.77321 1.075002 −0.90812 1.705817 1.075002 −0.18851 2.670449 1.075002 0.492465 3.655005 1.075002 1.136428 4.64877 1.075002 1.745896 5.641339 1.075002 2.323754 6.622913 1.075002 2.871074 7.585439 1.075002 3.389138 8.521265 1.075002 3.878877 9.423479 1.075002 4.340799 10.28597 1.075002 4.774608 11.1036 1.075002 5.180417 11.87154 1.075002 5.557611 12.58606 1.075002 5.905372 13.24415 1.075002 6.22283 13.84361 1.075002 6.509625 14.38275 1.075002 6.765227 14.86085 1.075002 6.989304 15.27797 1.075002 7.182054 15.63496 1.075002 7.343966 15.93346 1.075002 7.476094 16.17603 1.075002 7.579936 16.36606 1.075002 7.634537 16.51831 1.075002 7.608847 16.62828 1.075002 7.566416 16.6855 1.075002 7.522881 16.71866 1.075002 7.476994 16.73916 1.075002 7.41244 16.74983 1.075002 7.311039 16.72806 1.075002 7.204083 16.62496 1.075002 7.097792 16.45686 1.075002 6.962853 16.24204 1.075002 6.797465 15.97762 1.075002 6.600512 15.66132 1.075002 6.371403 15.2917 1.075002 6.109903 14.86799 1.075002 5.816301 14.39012 1.075002 5.490757 13.85896 1.075002 5.134071 13.27578 1.075002 4.746397 12.64305 1.075002 4.329168 11.96315 1.075002 3.882105 11.24013 1.075002 3.405835 10.47814 1.075002 2.900935 9.681908 1.075002 2.366746 8.857442 1.075002 1.803103 8.011015 1.075002 1.21004 7.149253 1.075002 0.586544 6.280009 1.075002 −0.0677 5.411245 1.075002 −0.75324 4.551686 1.075002 −1.47084 3.711015 1.075002 −2.2206 2.899218 1.075002 −3.00111 2.125919 1.075002 −3.81065 1.40151 1.075002 −4.64668 0.736909 1.075002 −5.5048 0.142517 1.075002 −6.37845 −0.37248 1.075002 −7.25876 −0.80096 1.075002 −8.13483 −1.13866 1.075002 −8.99433 −1.38477 1.075002 −9.82402 −1.54431 1.075002 −10.6116 −1.62673 1.075002 −11.3468 −1.64589 1.075002 −12.0224 −1.61764 1.075002 −12.6343 −1.55814 1.075002 −13.181 −1.48375 1.075002 −13.663 −1.40805 1.075002 −14.0819 −1.3429 1.075002 −14.4401 −1.30184 1.075002 −14.7387 −1.30611 1.075002 −14.9704 −1.36593 1.075002 −15.1197 −1.47217 1.075002 −15.195 −1.57986 1.075002 −15.2159 −2.78082 1.149997 −15.2112 −2.84457 1.149997 −15.1913 −2.93531 1.149997 −15.1342 −3.06687 1.149997 −15.0154 −3.22751 1.149997 −14.8207 −3.40121 1.149997 −14.5501 −3.58254 1.149997 −14.2022 −3.76559 1.149997 −13.7762 −3.94494 1.149997 −13.2715 −4.11352 1.149997 −12.6883 −4.26178 1.149997 −12.0279 −4.37737 1.149997 −11.2936 −4.44518 1.149997 −10.4916 −4.44765 1.149997 −9.632 −4.36518 1.149997 −8.72908 −4.18175 1.149997 −7.80018 −3.88557 1.149997 −6.86373 −3.47152 1.149997 −5.93524 −2.94443 1.149997 −5.02657 −2.31402 1.149997 −4.14602 −1.59255 1.149997 −3.30029 −0.79178 1.149997 −2.49387 0.076055 1.149997 −1.72964 0.998872 1.149997 −1.00767 1.963757 1.149997 −0.32586 2.957737 1.149997 0.317149 3.969707 1.149997 0.92289 4.989366 1.149997 1.494136 6.0065 1.149997 2.033569 7.011719 1.149997 2.543061 7.996734 1.149997 3.024113 8.953978 1.149997 3.477978 9.876546 1.149997 3.905535 10.75828 1.149997 4.306907 11.59391 1.149997 4.681928 12.37884 1.149997 5.030525 13.10913 1.149997 5.352001 13.78175 1.149997 5.645575 14.39442 1.149997 5.910981 14.94547 1.149997 6.147765 15.4341 1.149997 6.355511 15.86041 1.149997 6.53437 16.22526 1.149997 6.684729 16.53033 1.149997 6.807523 16.77823 1.149997 6.904066 16.97245 1.149997 6.953873 17.1266 1.149997 6.925334 17.23604 1.149997 6.88112 17.29205 1.149997 6.83651 17.32388 1.149997 6.789659 17.34299 1.149997 6.72434 17.35149 1.149997 6.623156 17.32572 1.149997 6.519613 17.21781 1.149997 6.419064 17.04467 1.149997 6.291793 16.82326 1.149997 6.135791 16.55078 1.149997 5.950002 16.22491 1.149997 5.733847 15.84422 1.149997 5.487061 15.40792 1.149997 5.209934 14.91599 1.149997 4.902475 14.36935 1.149997 4.565476 13.76931 1.149997 4.198773 13.11847 1.149997 3.803967 12.41916 1.149997 3.379903 11.67584 1.149997 2.928032 10.89217 1.149997 2.447824 10.07345 1.149997 1.939123 9.225327 1.149997 1.401708 8.353976 1.149997 0.834804 7.466442 1.149997 0.237554 6.570321 1.149997 −0.39066 5.673616 1.149997 −1.05004 4.784634 1.149997 −1.74118 3.912588 1.149997 −2.46415 3.067055 1.149997 −3.21774 2.257401 1.149997 −4.00021 1.493352 1.149997 −4.80868 0.784568 1.149997 −5.63924 0.14073 1.149997 −6.48587 −0.42983 1.149997 −7.34074 −0.92039 1.149997 −8.19423 −1.32656 1.149997 −9.0354 −1.64675 1.149997 −9.85209 −1.88436 1.149997 −10.6323 −2.04766 1.149997 −11.3659 −2.14823 1.149997 −12.0447 −2.19925 1.149997 −12.6634 −2.21606 1.149997 −13.2189 −2.21497 1.149997 −13.71 −2.20982 1.149997 −14.1368 −2.21175 1.149997 −14.4992 −2.23095 1.149997 −14.7954 −2.28246 1.149997 −15.0137 −2.38436 1.149997 −15.1414 −2.51733 1.149997 −15.1965 −2.63773 1.149997 −15.2131 −2.72187 1.149997

In the above Table 1, the plane Zadim=0 corresponds to the reference plane P0 situated at the base of the profile. This plane P0 is the intersection of the stacking axis AE of the set of vanes with the axisymmetric surface of the hub, i.e. it passes via the intersection between the axis AE and the surface where it is assembled with the inner shroud. The plane Zadim=1 corresponds to the reference plane P1 situated at the top of the profile. This plane P1 is the intersection between the axis AE and the axisymmetric surface of the casing, i.e. it passes via the intersection of the axis AE with the surface where it is assembled with the outer ring.

By convention, the stacking axis AE of a vane of a nozzle, is an axis that extends in the radial direction Z and is an axis on which the various X,Y sections of the set of vanes are “stacked” when designing the set of vanes.

As mentioned at the beginning of the present description, the aerodynamic profile of the disclosure is substantially identical to the nominal profile defined in the above table, i.e. it departs from said nominal profile by very little at most, being defined in particular within an envelope of ±1 mm in a direction normal to the surface of the nominal profile, and/or having X,Y coordinates lying within a range of ±5% relative to the coordinates X,Y of the nominal profile. Also, the aerodynamic profile is positioned rotated within ±10°, particularly within ±5°, more particularly within ±3°, with respect to the stacking axis of the vane. In other words, the stagger angle may vary by ±10°, particularly by ±5°, more particularly by ±3°.

The coordinate Zadim is non-dimensional, i.e. for a point P, situated at a distance D from the plane P0 (where D is measured along the axis Z), the value of Zadim is D/H, where H represents the total height of the profile as measured between the planes P0 and P1. Naturally, in the Table 1 above, by multiplying the coordinate Zadim by the height H, it is possible to obtain the complete coordinates of the vane.

By way of example, the total height H is preferably about 145 mm±10%. By way of example, the plane P0 is situated at a distance of about 405 mm±10% from the axis

A.

In the above table, the profile is characterized by fifteen section planes at constant Zadim coordinates, for which the coordinates X and Y are specified. These fifteen section planes include fifteen section planes located between Zadim=0 and Zadim=1, and thus arranged in the fluid stream, these section planes being distributed from P0 to P1. The fifteen section planes also include four section planes which are substantially outside the fluid stream (two section planes with Zadim<0, and two section planes with Zadim>1), these four section planes being provided for ensuring geometric continuity of the stacking, close to the head and the foot, respectively. In each section plane at constant coordinate Zadim, the section of the profile is given by a continuous and smooth curve, interconnecting all of the points (X,Y). In each section plane, the profile is interpolated so as to generate a uniform profile. Between the section planes, the profile is to be interpolated so as to generate a complete vane, as homogeneous as possible.

It is advantageous for the nozzle that includes the vane of the disclosure to have 135 to 155 vanes, more particularly 145 vanes, that present aerodynamic profiles as defined above. 

What is claimed is:
 1. A turbine vane configured to be mounted to a turbine, the turbine vane presenting an aerodynamic profile, defining the turbine vane when cold and in a non-coated state, the aerodynamic profile being substantially identical to a nominal profile determined by Cartesian coordinates X,Y,Zadim given in Table 1, in which coordinate Zadim is a quotient D/H, where D is a distance of a point under consideration from a reference X,Y plane situated at a base of the nominal profile, and H is a height of said nominal profile measured from said reference X,Y plane out to an end of the turbine vane, measurements D and H being taken radially relative to an axis of the turbine, while the coordinate X is measured in an axial direction of the turbine, wherein coordinates X and Y are expressed in millimeters (mm).
 2. The turbine vane as claimed in claim 1, wherein the turbine vane is a nozzle vane forming a part of a stator of the turbine.
 3. A turbine, including a plurality of turbine vanes as claimed in claim
 1. 4. The turbine as claimed in claim 3, including a nozzle that is stationary in rotation, having 135 to 155 turbine vanes that each presents the aerodynamic profile.
 5. The turbine as claimed in claim 3, including a nozzle that is stationary in rotation, having 145 turbine vanes that each presents the aerodynamic profile.
 6. A turbine nozzle forming a portion of a turbine stator, wherein the turbine nozzle includes a plurality of turbine vanes that each presents the aerodynamic profile as claimed in claim
 1. 7. The turbine nozzle as claimed in claim 6, including 135 to 145 turbine vanes.
 8. The turbine nozzle as claimed in claim 6, including 145 turbine vanes.
 9. A turbine vane configured to be mounted to a turbine, the turbine vane presenting an aerodynamic profile defining the turbine vane when cold and in a non-coated state, the aerodynamic profile corresponding to a nominal profile determined by Cartesian coordinates X,Y,Zadim given in Table 1, in which coordinate Zadim is a quotient D/H, where D is a distance of a point under consideration from a reference X,Y plane situated at a base of the nominal profile, and H is a height of said nominal profile measured from said reference X,Y plane out to an end of the turbine vane, measurements D and H being taken radially relative to an axis of the turbine, while coordinate X is measured in an axial direction of the turbine, wherein coordinates X and Y are expressed in millimeters (mm), wherein said aerodynamic profile is defined within an envelope of ±1 mm in a direction normal to a surface of the nominal profile, or the coordinates X,Y of said aerodynamic profile lie within a range of ±5% relative to the coordinates X,Y of the nominal profile.
 10. A turbine vane configured to be mounted to a turbine, the turbine vane presenting an aerodynamic profile defining the turbine vane when cold and in a non-coated state, the aerodynamic profile corresponding to a nominal profile determined by Cartesian coordinates X,Y,Zadim given in Table 1, in which coordinate Zadim is a quotient D/H, where D is a distance of a point under consideration from a reference X,Y plane situated at a base of the nominal profile, and H is a height of said nominal profile measured from said reference X,Y plane out to an end of the turbine vane, measurements D and H being taken radially relative to an axis of the turbine, while coordinate X is measured in an axial direction of the turbine, wherein coordinates X and Y are expressed in millimeters (mm), wherein the aerodynamic profile is positioned within ±10° with respect to a radial axis of the turbine vane.
 11. The turbine vane according to claim 10, wherein the aerodynamic profile is positioned within ±5° with respect to the radial axis of the turbine vane.
 12. The turbine vane according to claim 10, wherein the aerodynamic profile is positioned within ±3° with respect to the radial axis of the turbine vane. 